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Fungrim entry: f5e153

Symbol: PartitionsP p(n)p(n) Integer partition function
p(n)p(n) denotes the number of ways the integer nn can be written as a sum of positive integers.
Domain Codomain
nZn \in \mathbb{Z} p(n)Z0p(n) \in \mathbb{Z}_{\ge 0}
nZ0n \in \mathbb{Z}_{\ge 0} p(n)Z1p(n) \in \mathbb{Z}_{\ge 1}
Table data: (P,Q)\left(P, Q\right) such that (P)    (Q)\left(P\right) \implies \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
PartitionsPp(n)p(n) Integer partition function
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("f5e153"),
    SymbolDefinition(PartitionsP, PartitionsP(n), "Integer partition function"),
    Description(PartitionsP(n), "denotes the number of ways the integer", n, "can be written as a sum of positive integers."),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(n, ZZ), Element(PartitionsP(n), ZZGreaterEqual(0))), Tuple(Element(n, ZZGreaterEqual(0)), Element(PartitionsP(n), ZZGreaterEqual(1))))))

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2019-10-05 13:11:19.856591 UTC